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The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain…
When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex…
$\mathcal{G}$-structures, where $\mathcal{G}$ is a Lie group, are a uniform characterisation of many differential geometric structures of interest in supersymmetric compactifications of string theories. Calabi-Yau $n$-folds are instances of…
Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with…
We present a uniform description of $\mathrm{SU}(3)$-structures in dimension $6$ as well as $G_2$-structures in dimension $7$ in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to…
We characterize spin initial data sets that saturate the BPS bound in the asymptotically AdS setting. This includes both gravitational waves and rotating black holes in higher dimensions, and we establish a sharp dimension threshold in each…
Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the…
This thesis is devoted to the construction of theories describing the consistent propagation of (super)conformal higher-spin fields on curved three- and four-dimensional (super)spaces. In the first half of this thesis we systematically…
We give a world-sheet description of D-brane in terms of gluing conditions on T+T^*. Using the notion of generalized Kahler geometry we show that A- and B-types D-branes for the general N=(2,2) supersymmetric sigma model (including a…
In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N=4 gauged supergravity. We perform this general SU(2) reduction and give…
We find the conditions on compactifications of type IIA to four-dimensional Minkowski space to preserve N=2 supersymmetry in the language of Exceptional Generalized Geometry (EGG) and Generalized Complex Geometry (GCG). In EGG, off-shell N…
We consider type II (non-)geometric flux backgrounds in the absence of brane sources, and construct their explicit embedding into maximal gauged D=4 supergravity. This enables one to investigate the critical points, mass spectra and gauge…
We propose a generalization of the (conformal) Killing-Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form *F, couples naturally to particles in…
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum $G_2$ manifolds. For a given $G_2$ manifold, we discuss evidence for the existence of mirror symmetries of two kinds:…
In this paper we study M-theory compactifications on manifolds of G2 structure. By computing the gravitino mass term in four dimensions we derive the general form for the superpotential which appears in such compactifications and show that…
The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further…
We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity. Such rotating black holes admit an AdS$_2$ near-horizon geometry which is…
We describe three analytic classes of infinitely many AdS_d supersymmetric solutions of massive IIA supergravity, for d = 7, 5, 4. The three classes are related by simple universal maps. For example, the AdS_7 x M_3 solutions (where M_3 is…
Supersymmetric backgrounds in M-theory often involve four-form flux in addition to pure geometry. In such cases, the classification of supersymmetric vacua involves the notion of generalized holonomy taking values in SL(32,R), the Clifford…
We study conditions on general fluxes of massive Type IIA supergravity that lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these conditions in the case of SU(3)- as well as SU(2)-structures. SU(3)-structures imply…